Finite Group Databasebeta

← C103×#10149 #39915424

Subgroups — C103×#10149 #39915424

Order 26368.

528 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3230C211yesmaximal, characteristic, complemented
2C103×#3138C211yesmaximal, characteristic
3C2×#486×C103C211yesmaximal, characteristic
4C103×#1997C211yesmaximal, characteristic, complemented
5C103×#1545C211yesmaximal, characteristic
6C103×#1493C211yesmaximal, characteristic, complemented
7C103×#1278C211yesmaximal, characteristic, complemented
8#533×C103C2211yescharacteristic
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×#127×C103C2211yescharacteristic
11#500×C103—21no—
12#490×C103—22no—
13#487×C103—21no—
14#486×C103—21no—
15#486×C103—21no—
16#486×C103—22no—
17#486×C103—22no—
18#484×C103—22no—
19#477×C103—22no—
20#431×C103C2211yescharacteristic
21#423×C103C2211yescharacteristic
22#418×C103—22no—
23C2×#102×C103—22no—
24C4×M16×C103C2211yescharacteristic
25C2×C4×C8×C103C2211yescharacteristic
26#343×C103—22no—
27#331×C103—22no—
28Q8⋊C8×C103—22no—
29C22×Q8×C103—21no—
30C22×D4×C103—21no—
31C22×D4×C103—21no—
32C22×D4×C103—21no—
33C2×M16×C103—21no—
34C2×M16×C103D412yes—
35C22×C8×C103—21no—
36C4⋊Q8×C103—21no—
37C4⋊Q8×C103—21no—
38C4⋊Q8×C103—21no—
39C4⋊Q8×C103—21no—
40C4⋊Q8×C103D411yescharacteristic
41C4⋊Q8×C103D411yescharacteristic
42#127×C103—21no—
43#127×C103—21no—
44#127×C103—21no—
45#127×C103D412yes—
46#125×C103—21no—
47C22⋊Q8×C103—21no—
48C22⋊Q8×C103—21no—
49C4×Q8×C103—21no—
50C4×Q8×C103—21no—
51#117×C103—21no—
52C2×C4⋊C4×C103—21no—
53C2×C4⋊C4×C103D412yes—
54C2×C42×C103C2311yescharacteristic
55#107×C103—24no—
56C4⋊C8×C103—21no—
57C4⋊C8×C103—21no—
58C4⋊C8×C103D412yes—
59#103×C103—24no—
60#102×C103—28no—
61#102×C103—24no—
62#102×C103—24no—
63C22⋊C8×C103—21no—
64#97×C103—21no—
65C4×C8×C103—21no—
66C4×C8×C103—21no—
67C4×C8×C103—21no—
68C4×C8×C103D412yes—
69C24×C103—41no—
70C2×Q8×C103—21no—
71C2×Q8×C103—21no—
72C2×Q8×C103—41no—
73C2×Q8×C103—41no—
74C2×Q8×C103—82no—
75C2×D4×C103—22no—
76C2×D4×C103—22no—
77C2×D4×C103—22no—
78C2×D4×C103—44no—
79C2×D4×C103—41no—
80C2×D4×C103—41no—
81C2×D4×C103—41no—
82C2×D4×C103—42no—
83C2×D4×C103—42no—
84C2×D4×C103—82no—
85C22×C4×C103—22no—
86C22×C4×C103C2×D411yescharacteristic
87C22×C4×C103C2×D411yescharacteristic
88C22×C4×C103#4111yescharacteristic
89M16×C103—22no—
90M16×C103—22no—
91M16×C103—42no—
92C2×C8×C103—22no—
93C2×C8×C103—22no—
94C2×C8×C103—22no—
95C2×C8×C103—42no—
96C2×C8×C103—41no—
97C4⋊C4×C103—22no—
98C4⋊C4×C103—21no—
99C4⋊C4×C103—21no—
100C4⋊C4×C103—22no—
101C4⋊C4×C103—21no—
102C4⋊C4×C103—21no—
103C4⋊C4×C103—41no—
104C4⋊C4×C103—41no—
105C4⋊C4×C103—41no—
106C4⋊C4×C103—41no—
107C22⋊C4×C103—41no—
108C42×C103—41no—
109C42×C103C2×D411yescharacteristic
110C42×C103C2×D411yescharacteristic
111C42×C103C2×D411yescharacteristic
112C42×C103C2×D411yescharacteristic
113C23×C103—42no—
114C23×C103—82no—
115C23×C103—82no—
116C23×C103—82no—
117C23×C103#12111yescharacteristic
118Q8×C103—42no—
119Q8×C103—42no—
120Q8×C103—82no—
121Q8×C103—82no—
122D4×C103—44no—
123D4×C103—44no—
124D4×C103—82no—
125D4×C103—82no—
126D4×C103—82no—
127D4×C103—81no—
128D4×C103—81no—
129C2×C4×C103—22no—
130C2×C4×C103—22no—
131C2×C4×C103—41no—
132C2×C4×C103—41no—
133C2×C4×C103—42no—
134C2×C4×C103—82no—
135C2×C4×C103#12011yescharacteristic
136C2×C4×C103#12011yescharacteristic
137C2×C4×C103#12011yescharacteristic
138C2×C4×C103#12111yescharacteristic
139C2×C4×C103#12111yescharacteristic
140C2×C4×C103#12711yescharacteristic
141C2×C4×C103#13512yes—
142C2×C4×C103#13712yes—
143C8×C103—42no—
144C8×C103—42no—
145C8×C103—42no—
146C8×C103—81no—
147C22×C103—21no—
148C22×C103—21no—
149C22×C103—82no—
150C22×C103—82no—
151C22×C103—82no—
152C22×C103—164no—
153C22×C103#39211yescharacteristic
154C22×C103#46412yes—
155C4×C103—21no—
156C4×C103—21no—
157C4×C103—81no—
158C4×C103—82no—
159C4×C103—81no—
160C4×C103#45212yes—
161C4×C103#45412yes—
162C4×C103#47212yes—
163C4×C103#49511yescharacteristic
164C4×C103#49711yescharacteristic
165#10149C10311yesmaximal, characteristic, direct product factor, Sylow
166C2×C103—22no—
167C2×C103—162no—
168C2×C103#200311yescharacteristic
169C2×C103#201511yescharacteristic
170C2×C103#201811yescharacteristic
171#3230C2×C10311yescharacteristic, complemented
172#3138C2×C10311yescharacteristic
173C2×#486C2×C10311yescharacteristic
174#1997C2×C10311yescharacteristic, complemented
175#1545C2×C10311yescharacteristic
176#1493C2×C10311yescharacteristic, complemented
177#1278C2×C10311yescharacteristic, complemented
178C103#1014911yescharacteristic, direct product factor, Sylow
179#533C22×C10311yescharacteristic
180C2×C4⋊Q8C22×C10311yescharacteristic
181C2×#127C22×C10311yescharacteristic
182#500—21no—
183#490—22no—
184#487—21no—
185#486—21no—
186#486—21no—
187#486—22no—
188#486—22no—
189#484—22no—
190#477—22no—
191#431C22×C10311yescharacteristic
192#423C22×C10311yescharacteristic
193#418—22no—
194C2×#102—22no—
195C4×M16C22×C10311yescharacteristic
196C2×C4×C8C22×C10311yescharacteristic
197#343—22no—
198#331—22no—
199Q8⋊C8—22no—
200C22×Q8—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C2×M16—21no—
205C2×M16D4×C10312yes—
206C22×C8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8D4×C10311yescharacteristic
212C4⋊Q8D4×C10311yescharacteristic
213#127—21no—
214#127—21no—
215#127—21no—
216#127D4×C10312yes—
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222#117—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4D4×C10312yes—
225C2×C42C23×C10311yescharacteristic
226#107—24no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8D4×C10312yes—
230#103—24no—
231#102—28no—
232#102—24no—
233#102—24no—
234C22⋊C8—21no—
235#97—21no—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8D4×C10312yes—
240C24—41no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—82no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—44no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—82no—
256C22×C4—22no—
257C22×C4C2×D4×C10311yescharacteristic
258C22×C4C2×D4×C10311yescharacteristic
259C22×C4#41×C10311yescharacteristic
260M16—22no—
261M16—22no—
262M16—42no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—42no—
267C2×C8—41no—
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C22⋊C4—41no—
279C42—41no—
280C42C2×D4×C10311yescharacteristic
281C42C2×D4×C10311yescharacteristic
282C42C2×D4×C10311yescharacteristic
283C42C2×D4×C10311yescharacteristic
284C23—42no—
285C23—82no—
286C23—82no—
287C23—82no—
288C23#121×C10311yescharacteristic
289Q8—42no—
290Q8—42no—
291Q8—82no—
292Q8—82no—
293D4—44no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—82no—
298D4—81no—
299D4—81no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4#120×C10311yescharacteristic
307C2×C4#120×C10311yescharacteristic
308C2×C4#120×C10311yescharacteristic
309C2×C4#121×C10311yescharacteristic
310C2×C4#121×C10311yescharacteristic
311C2×C4#127×C10311yescharacteristic
312C2×C4#135×C10312yes—
313C2×C4#137×C10312yes—
314C8—42no—
315C8—42no—
316C8—42no—
317C8—81no—
318C22—21no—
319C22—21no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—164no—
324C22#392×C10311yescharacteristic
325C22#464×C10312yes—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—82no—
330C4—81no—
331C4#452×C10312yes—
332C4#454×C10312yes—
333C4#472×C10312yes—
334C4#495×C10311yescharacteristic
335C4#497×C10311yescharacteristic
336C2—22no—
337C2—162no—
338C2C103×#200311yescharacteristic
339C2C103×#201511yescharacteristic
340C2C103×#201811yescharacteristic
subgroupG/H
center, socleC22×C103#392
commutator, Frattini, cosocleC2×C42C23×C103
prime radicalC2×#127×C103C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C103×#3230C2semidirect
4. C103×#1997C2semidirect
6. C103×#1493C2semidirect
7. C103×#1278C2semidirect
165. #10149C103direct (N × H)
171. #3230C2×C103semidirect
174. #1997C2×C103semidirect
176. #1493C2×C103semidirect
177. #1278C2×C103semidirect
178. C103#10149direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C103×#32302
C103×#31382
C2×#486×C1032
C103×#19972
C103×#15452
C103×#14932
C103×#12782
#10149103